Logs have always been a hard concept to get across to students. I learned a helpful tool in my pre calculus class my junior year of high school that has not only helped me from that point on but everyone who I have taught since then. I call it the swoosh rule. I am in the process of finding any copyright owners but I believe that the title will soon be the Casci Swoosh Rule. The swoosh rule helps with the following problem.
The hardest obstacle for students to get over is the conversion between an equation in logarithmic form and an equation in exponential form. The swoosh rule is a fun drawing technique that helps the student remember where the components of the log function go in the exponential function.
This will help the student remember that the exponent function is the base of the log function raise to the solution of the log function and that it equals the term/quantity of what you are taking the log of. When teaching it helps to say what your doing. For example, for the problem above, you would say, “a raise to the c equals b.”
Performing the swoosh rule the opposite way has some variety and really can be done in a couple of different ways. My favorite is using the “swoosh” in the same direction as the technique shown above only with the exponential equation.
Again it is helpful to say, “log base a of b equals c.” I think this is the best way of going from an exponential function to a log function because it the same swoosh motion as the original conversion from logs to exponents. There is another variation that I have found but is not as affective. Enjoy!
Here is a great site for checking your work. It is a logrithmic calculator.
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